Are there alternatives to software center?

Yes, there is an alternative to the Ubuntu Software Center named appgrid. It's a very lightweight application center for Ubuntu and it will let you purchase applications too. You can install it in Ubuntu with these following commands:

sudo add-apt-repository ppa:appgrid/stable
sudo apt-get update
sudo apt-get install appgrid

It was only a 100KB download for me.

Comparison between appgrid and Ubuntu Software Center:

Feature                                                | appgrid  | Ubuntu Software Center
-------------------------------------------------------+----------+-----------------------
Programming language                                   | Python 3 | Python 2
Warm start to home screen                              | 2.7s     | 20s
Warm start to details screen (eg opening an apt: link) | 2.3s     | 30s
Full database build                                    | 58s      | 6min24
Initial database size                                  | 36.7MB   | 96.5MB
Memory usage after startup to home screen              | 20MB     | 53.6MB
Lines of code (including tests)                        | 5900     | 56960

You can sign in with Ubuntu One ID also:

You can use synaptic , a front-end for apt-get.

Yes. Try the Lubuntu Software Center. It is very fast and light-weight.

sudo apt-get install lubuntu-software-center